Problem: Simplify the following expression: $ y = \dfrac{-5}{4} + \dfrac{-7x - 6}{-2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2}{-2}$ $ \dfrac{-5}{4} \times \dfrac{-2}{-2} = \dfrac{10}{-8} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-7x - 6}{-2} \times \dfrac{4}{4} = \dfrac{-28x - 24}{-8} $ Therefore $ y = \dfrac{10}{-8} + \dfrac{-28x - 24}{-8} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{10 - 28x - 24}{-8} $ $y = \dfrac{-28x - 14}{-8}$ Simplify the expression by dividing the numerator and denominator by -2: $y = \dfrac{14x + 7}{4}$